In particular, the potential \(\sum _{1 \le j \le N} \frac{b_j}{|x_j|}+ \sum _{1 \le i < j \le N} \frac{c_{ij}}{|x_i-x_j|}\)  considered in
the study of the \(N\) -body problem is an inverse square potential with
singularities on the collision planes (more precisely, on the semilattice
generated by the collision planes).
Moreover, the inverse square potentials considered in
[1]}, [2]}, [3]}, [4]}, [5]} are also
inverse square potentials in our sense.
